Except...for a start, the headline is about the owner of a private jet company attempting to defend the environmental credentials of his services. Hardly an unbiased statement.
However, let's take it at face value (and ignore the fact that there are no actual citations in the article, which is odd given that the source is a university). They state that a dog has 98% of the carbon footprint of a Brazilian citizen. That's 2.28 tonnes per year, as opposed to 5.2 tonnes for a UK citizen. How they come to that conclusion given the massive disparity in dog sizes is unknown (did they take the median, or the mean? Or just wave a finger in the air?), because there are no citations, but fine. That's 42.9% of a person, which seems ludicrously high given the weight disparity and the fact that they don't drive, but of course we also don't know if they also took into account the fact that dog food production largely uses byproducts from human food production processes (I very much doubt it).
Dogs also live 13% as long as humans. So...the actual carbon footprint of a dog is 5.79% that of a human in the UK.
Now, when you look a bit deeper, it turns out that the figures they quote are the highest you can possibly find anywhere (see the first point about the main statement coming from the owner of a private jet company, I guess). The consensus seems to be that the median dog has a carbon footprint of around 770kg/year, which is a massive difference, and changes that 5.79% to 1.9%.
So...yeah, turns out that article can be safely ignored. If you don't like dogs, just say so and it would probably have more meaning than that article (but this thread probably isn't for you).